Introduction to
Teaching Statistics
at the Community
Colleges
June 2006
Jackie Dacosta
Mahtash Esfandiari
Overview of Community Colleges
in Los Angeles Area
‣ There are 21 community colleges in the Los
Angeles area.
- 9 of these colleges are part of the Los
Angeles Community College District.
‣ Most colleges are on semester system with 15
-18 weeks
‣ Most colleges try to adhere to a full-time to part-
time faculty ratio of 75: 25 within their college. In
practice, the percentage of full-time math and
statistics instructors may be as low as 60%.
‣ Why Students Attend Community Colleges
- Transfer to a Cal State or UC
- Pursue a 2 year Associate degree
- Obtain certification or vocational training
- Other
Statistics Courses at Community
Colleges in Los Angeles Area
‣ The number of statistics courses offered at
community colleges is rising.
‣ Each college offers 2-15 sections of introductory
statistics per semester: about 25% night courses,
5% online courses.
‣ Some colleges offer honors math courses. Few
offer honors statistics courses.
‣ Introductory statistic courses are labeled as math
courses in the schedule of classes. Thus,
students often refer to a statistic course as a
math course.
‣ The introductory statistics courses varies from 3
‣
-4 semester units.
2-12 different instructors teaching statistics per
college
Note: Statistics for Social Sciences, Economics,
Business were not part of our study
Objectives of the Study
‣ An overview of how statistics is taught at the
community colleges through detailed analysis of
- most commonly used textbooks for teaching
introductory statistics
- typical syllabi and their alignment with GAISE
- typical teacher made exams
- one-on-one interviews with community
college instructors
Textbook Review
Objective
‣The objective of this part of the presentation is to
do an in-depth analysis of two textbooks (Triola
and Sullivan) used in teaching introductory
statistics in community college. Triola is used by
80% to 90% of the community colleges in Los
Angeles. This analysis is based on in-depth
examination of the chapters written on exploratory
data analysis, sampling design and design of
experiments.
I. Introducing Statistics as a
“Science of Data”
6
II. Presentation of Material
7
II. Presentation of Material (cont’d)
8
Sample Definition of Statistical
Concepts
Triola
‣ “The arithmetic mean of a set of values is the number
obtained by adding the values and dividing the total by
the number of values.”
‣ “Variation refers to the amount that values vary among
themselves, and it can be measured with specific
numbers.”
‣ “The variance of a set of values is a measure of variation
equal to the square of the standard deviation.”
‣ “Standard deviation of a set of samples is a measure of
variation of values about the mean and it can be
calculated by formula..”
Sullivan
‣ “The arithmetic mean of a variable is computed by
determining the sum of all the values of the variable in
the data set, divided by the number of observations.”
‣ “Variance is based upon the difference between each
observation and the arithmetic mean; that is, it is based
upon the deviations about the mean.”
‣ “Standard deviation is obtained by taking the square of
the variance.”
Sample Definitions from Sullivan
are Incomplete and Vague:
‣
Quantitative categorical variables allow for the classification of
individuals based on some attribute or characteristic.
‣
Quantitative variables provide numerical measures of individuals.
Arithmetic operations such as addition and subtraction can be
performed on the values of quantitative variables and provide
meaning results.
‣
If performing arithmetic operation is the distinguishing feature
of the quantitative variables, then in the definition of qualitative
variables, it should be clarified that such operations cannot be
performed.
‣
An observational study measures the characteristics of the
population by studying individuals in a sample, but does not attempt
to manipulate the variables (s) of interest. Observational studies are
sometimes referred to as ex post facto (after the fact) studies
because the value of the variable of interest has already been
established.
‣
‣
No mention of how the subjects are selected.
‣
‣
No mention of random assignment or how the groups are formed.
‣
This is vague. How would you go about selecting these groups?
A designed experiment applies a treatment to individuals (referred
to as experimental units) and attempts to isolate the effect of
treatment as response variable.
Cluster sampling: A cluster sample is obtained by selecting all
individuals within a randomly selected collection or group of
individuals.
III. Exercises at the End of the
Chapter
11
IV. Use of Technology
12
Overall Comments about Sullivan
‣"
‣"
Clear objectives at the beginning of each section
‣"
Good modeling of what the students are expected to do in
solving problems at the end of the chapter
‣"
Definitions come before “case studies”. It make more
sense to have definitions come after the case studies. For
example, terms like “ex-post facto” make much more
sense after the students have read a scenario. When the
students see a definition, they may try to memorize it
without understanding it, When reading the “case study”
first helps to set the stage for the definition and clarifies it
‣"
Definitions are sometimes incomplete. For instance, there
is no mention of lack of randomization in the description
of observational studies.
‣"
There are some, but not enough modeling of what the
students need to do with respect to the interpretation of
the plots within context as well as problems that involve
upper level thinking.
‣"
More emphasis needs to be placed on writing and
interpretation of data from histograms. The questions are
more abut eyeball estimation of percentages.
Proper scaffolding and creation of tie between the old and
the new: Under a part entitled “preparing for this section”,
reminds the students of the concepts they need to know
as well as the pages and sections that they need to refer
to.
13
Overall Comments about Triola
‣"
Too much emphasis is placed on calculations, around nine pages
are spent on describing how to calculate mean and standard
deviation with data presented as frequency tables.
‣"
Verbal explanations, plots and equations are used to clarify
computation and not concepts.
‣"
Exercises are mostly computational. In the exercise section,
there is a part entitled Basic Skills that is mainly computations
and a part entitled Beyond the Basics which has more
complicated calculations.
‣"
Not enough attention is paid to concepts. For instance, not
enough attention is paid to important concepts in design and
sampling. Design and sampling are covered in nine pages.
‣"
Definitions are basically verbalization of the mathematical
symbols and not clarification of the concepts.
‣"
Questions about sampling and design are mostly recall of
information and recognition of sampling. There are no exercises
on suggestion of proper method of sampling or whether the
sampling method proposed is appropriate.
‣"
Cooperative group exercises, internet projects, and critical
thinking questions are included at the end of the chapter.
However, none of the above is modeled or referred to in the
chapter. It is assumed that the students automatically develop
the above competencies.
‣"
Students are expected to construct plots rather than comment on
the plots created by the computer.
‣"
No modeling of what the students are expected to do in thinking
exercises. Interpretation of plots and tables is offered.
14
Summary of Textbook Review
Based on the above analysis, I think Sullivan is relatively
more generative in nature compared to Triola because it
places more emphasis on:
‣"
‣"
‣"
Making sure that the students have the pre-requisite
information for acquiring new concepts,
Modeling the tie between the different dimensions of
statistics including data sets, printout, and plots, and
Providing the students with a chance to think about
statistical concepts and methods, and engaging in
when and where these concepts and methods
applied.
15
Data Gathered
‣ 9 syllabi and 14 exams were collected from 9
instructors teaching in 6 colleges
•
•
The exams analyzed consisted of 80%
exploratory data analysis, sampling, design of
experiments, measures of center and spread,
plots, visuals
In order to examine the alignment between the
textbooks and the teacher made exams, we used
textbooks chapters corresponding to concepts
covered in the exams analyzed
‣ Interviewed 11 instructors from 7 colleges
-
10 were full time instructors,
respondents were asked 22 questions regarding
their teaching experiences in statistics,
interviews lasted 20-60 minutes, and
9 were conducted in person, 3 were conducted
via phone.
Background of Instructors
Interviewed
‣
‣
‣
‣
‣
‣
‣
‣
Degrees (11 instructors)
8 full-time instructors hold a master degree in Applied
Math, Math, or Pure Math
2 full-time instructors hold a master degree in Math
and Education (former high school math teachers)
1 part-time instructor has a master degree in Statistics
Teaching Experience at the College Level
Average number of statistics courses taken in college:
2.8
Average numbers of years teaching math at
community college (or university): 7
Average numbers of years teaching statistics at
community college (or university): 4.4
Only one instructor has experience in a statistics
related occupation
5 have attended a statistics workshop within the past 5
years
Background of Students
Based on interviews with instructors:
‣ Some students choose to take statistics instead
of a traditional math class to fulfill math
requirements with expectations that
- Statistics is not as mathematical
- They will learn something that is useful in the
real world
‣ For many students, this is the last ‘math’ course
that they will take in college.
‣ Some students wait until the last semester before
transferring or graduating (Spring) to take the
course.
‣ Many community college students are dependent
learners. They can learn as long as the
instructors guide them.
Guidelines for Assessments and
Instruction in Statistics Education
‣ In November 2005, the American Mathematical
Association of Two-Year Colleges (AMATYC)
endorsed (GAISE)
‣ AMATYC offered one workshop for preparing two
year college instructors to teach with GAISE
-
Only 30 seats were available and “filled within
hours”
Six Core Recommendation in GAISE
‣ Emphasize statistical literacy and develop
statistical thinking
‣ Use real data.
‣ Stress conceptual understanding rather than
mere knowledge of procedures.
‣ Foster active learning in the classroom.
‣ Use technology for developing concepts and
analyzing data.
‣ Use assessments to improve and evaluate
student learning.
Syllabus for Introductory Statistics
‣ GAISE has published a sample syllabus
[handout]
‣ It is important for an introductory statistics course
to have a thorough syllabus so that students are
immediately aware that statistics is very different
from the traditional math courses, that is when
taught correctly or according to GAISE.
‣ Instructors need to spell out for the students
‣ the goals/objectives of the course
‣ what active learning is and how to be an
‣
active learner
what statistical thinking is and how to achieve
this
‣ We examined 11 introductory statistic syllabi from
the community colleges.
GAISE Syllabus vs Community
College Syllabus
GAISE
Community College
short description for intended
audience
prerequisites for the course
detailed course goals and
objectives
course ‘catalog’ description of
overall content
list of course materials
similar
instructional format (active
learning warning)
attendance, class participation,
group work
detailed course requirements of
what students is expected to
demonstrate
course requirements includes
details around homework
assignments, labs, etc
detailed grading breakdown
similar
detailed course schedule with
titles of chapters
course schedule with section
numbers
lesson goals and objectives
None. Some pass out lesson plans
later
How to get help: encourages
students to come to office hours,
form study groups, etc
Disciplinary action: code of
conduct, behavior
Overall Course Goals (not found in
Typical Community College
Syllabi)
Course goals articulated by instructors during
interviews:
‣ Describe the differences between descriptive and
inferential statistics
‣ Know how probability works as a tool in statistics
‣ When encountering statistics from the media,
• to look more critically at charts and data
• ask key questions in order to examine
‣
conclusions/statistics more closely
Enjoy statistics
‣ Conclusion: Although this is not written in the
syllabus, the instructors’ attitudes are aligned
with the new trends in statistics education
Instructors’ Input Regarding Triola
‣ 80-90% of the colleges in Los Angeles area are
‣
using Elementary Statistics by Triola
There is a preference to using the same textbook
in the region because many part-time instructors
teach at multiple colleges
Effectiveness of textbook as perceived by
instructors
‣ 7 instructors interviewed were using Triola.
‣ Mixed responses on instructor’s input regarding
the Triola textbook.
- 3 out of 7 do not find the book effective
because they felt that it was not written for
the students.
- 4 out of 7 find the book somewhat effective
because they feel that it is easily understood
by the students. Many of the instructors feel
that the minitab exercises, Triola lecture
videos and student supplements are helpful.
- Within each divide, there are 2 instructors
who are aware of GAISE.
GAISE Recommendations on
Assessments
‣
‣
‣
‣
‣
‣
‣
‣
‣
‣
GAISE
Recommendation 6: Use assessments to improve and
evaluate student learning.
Students will value what you assess. Therefore assessments
need to be aligned with learning goals. Assessments need to
focus on understanding key ideas and not just on skills,
procedures, and computed answers. This should be done
with formative assessments used during a course (e.g.,
quizzes and midterm exams and small projects) as well as
with summative evaluations (course grades). Useful and
timely feedback is essential for assessments to lead to
learning. Types of assessment may be more or less practical
in different types of courses. However, it is possible, even in
large classes, to implement good assessments.
Types of assessment:
Homework
Quizzes and exams
Projects
Activities
Oral Presentations
Written reports
Minute papers
Article critiques
Classification of Exam Questions
After detailed examination of teacher made
exams, questions were classified into 3 major
categories:
‣ Computation problems
‣ Word problems
‣ Problems involving tables and/or graphs
- Within each category, we broke it down
‣
‣
‣
‣
further by classifying problems into 3 levels
(I, II, III) keeping in mind that:
All exams were closed books
All (except for 2 exams) allowed formula sheets
provided by the textbooks or the instructors
TI-83 calculators were allowed
Some problems were multiple choice
Criteria for Classification of
Computation Problems
‣ Level I: Given the data, use a basic formula to
do carry out the relevant calculations. Example:
Given a set of data, compute mean, variance,
standard deviation, etc.
‣ Level II: Given a relatively simple scenario,
identify the givens that are necessary for the
computation, and use the relevant formulas to
carry out the computation.
‣ Level III: Given a complex scenario, analyze it
and identify the different parts, specify the givens
needed to solve the problem, and apply the
relevant formulas to carry out the relevant
computation.
Criteria for Classification of Word
Problems
‣
Level I: Recall, define, and recognize facts/concepts.
‣
Level II: Comprehension by putting some conclusion
or observation in their own words to
- show understanding of information
- translate meaning into new context
- interpret simple facts, simple compare/contrast.
‣
Level III: Analyze, interpret, explain, evaluate and
synthesize. This may require
- breaking an idea into parts such that the
relationship is made clear
- putting pieces together to construct a pattern or
idea by relating knowledge from several areas
- making decisions about the materials or methods
(ie. compare and discriminate between ideas)
- making decisions based on evidence, verify value
of evidence and recognize subjectivity.
Criteria for Classification of
Problems Involving Tables and
Graphs
‣ Level 1: Draw a graph based on data or carry out
calculations from tables or graph.
‣ Level II: Describe properties of the given table/
graph, interpret a table/graph, compare table/
graphs, choose appropriate graphs, and show
relationship between graph and data.
‣ Level III: Compare and discriminate between
graphs, describe patterns in graph, recognize
‘hidden’ meanings in graphs, relate knowledge
from several areas, draw conclusions and make
decisions based on graphs/tables
Classification of Questions Given by 3
Instructors on Exploratory Data Analysis and
Basic Probability Concepts
Instructor using the Triola textbook had an average of
-
76.47 % Computation Questions
-
0 % Word Problems
-
23.53 % Problems with Tables and/or Graphs
Instructor using the Triola textbook and GAISE ha d an
average of
-
28.86 % Computation Questions
-
38.41 % Word Problems
-
32.73 % Problems with Tables and/or Graphs
Instructor using the Sullivan textbook had an average of
-
45.17 % Computation Questions
-
30.88 % Word Problems
-
23.95 % Problems with Tables and/or Graphs
Classification of Questions Given by 3
Instructors on Exploratory Data Analysis and
Basic Probability Concepts
Calc
Instructor I
Triola
Calc
II
20.59 55.88
Calc
III
0.00
Word Word Word Table Table Table
Prob Prob Prob Graph Graph Graph
I
II
III
I
II
III
0.00
0.00
0.00
23.53
0.00
0.00
Triola w/
GAISE
0.00 15.82 13.04
2.78 28.50
7.13
2.17
16.67
13.89
Sullivan
11.87 17.12 16.18
7.14 18.38
5.36
13.03
10.92
0.00
Percentages reported in the above table are averages
of 2 exams
Classification of Questions Given by 8
Instructors on Exploratory Data Analysis and
Basic Probability Concepts
Instructors using the Triola textbook had an average of
-
56.15 % Computation Questions
-
27.31 % Word Problems
-
16.55 % Problems with Tables and/or Graphs
Instructor using the Triola textbook and GAISE had an
average of
-
28.86 % Computation Questions
-
38.41 % Word Problems
-
32.73 % Problems with Tables and/or Graphs
Instructors using the Sullivan textbook had an average of
-
34.61 % Computation Questions
-
42.30 % Word Problems
-
23.09 % Problems with Tables and/or Graphs
Classification of Questions Given by 8
Instructors on Exploratory Data Analysis and
Basic Probability Concepts
Calc
Instructor I
Triola (4)
Calc
II
15.92 38.88
Calc
III
Word Word Word
Prob Prob Prob
I
II
III
Table
Grap
h
I
Table Table
Graph Graph
II
III
3.49
5.03 13.39
6.17
14.34
2.23
0.56
Triola w/
GAISE (1)
0.00 15.82 13.04
2.78 28.50
7.13
2.17
16.67
13.89
Sullivan
(3)
9.32 18.79
6.5 12.88 23.32
6.10
16.58
5.53
0.98
Percentages reported in the above table are averages.
Instructors’ Perception Regarding
Challenges in Teaching Statistics
‣
Many instructors come in with little or no statistics
training.
‣
Lack of clear standards regarding teaching statistics
course.
‣
One instructor felt that some instructors have the
misconception that standards are related to students
learning the same way they did.
‣
Some instructors acknowledge the importance of
diagnostic evaluation: evaluating their students’
baseline knowledge prior to starting the course.
‣
Some instructors are aware of the importance of the
role that students play in their own learning. For
instance, one said “it not about what I teach; it's about
what the students learn.”
Most instructors are familiar with the importance of
using real data and technology but sometimes find it
difficult to do this
‣
Instructors’ Perception Regarding
Student Learning
‣
Diverse student body ( ie. full-time workers, parenting,
older students)
• Varying math skills
• Varying study skills (ie. returning to school after 15
-20 years)
‣
Difficult to motivate some students to do homework
‣
Technology Divide: some of them work well with
technology and some cannot even use the TI-83
calculator.
Economic Divide: some can't afford TI-83, especially
not for just one terminal statistics course
‣
‣
Students may easily mistaken the course to be a broad
survey course versus an introductory course since
instructors rush to cover all the 'recommended'
chapters which leads to insufficient time for students to
absorb and reflect.
‣
Some are surprised to see how conceptual the course
is. “I was never asked to think in a math course until
now. . “.
Strategies that Instructors
Implement to Teach Diverse
Audience
‣ Many instructors do not feel that they are
lowering the standards even though students
have varying learning skills, math skills and time
commitment.
‣ They have a variety of instructional methods:
lectures, discussion, group activities, quizzes and
projects
‣ Encourage students to come office hours and to
form study groups
‣ In addition to exams, administer quizzes to test
basic statistics skills that are essential for survive
in the course. At first students despise this but
later appreciate this because they realize what
they need to work on.
Instructors’ Use of Existing
Reference Materials
‣ Many are aware of other online reference
materials regarding active learning and real
datasets. However, some of them reported that
they did not have time to fully explore.
‣ Some of them didn’t find the online materials
helpful or quickly adoptable.
‣ Most of them are not aware that there are
workshop materials on implementing GAISE.
Willingness to Learn about GAISE
vs Willingness to Implement
‣ 9 out of 11 were interested in learning about the
GAISE or new trends. Two instructors seemed
uninterested or reluctant to learn due to lack of
time or slight resistant to change.
‣ 8 out of 11 of the instructors interviewed seemed
willing to implement some part of the GAISE or
new trends if they had some examples to adopt
or clear guidance. Three instructors did not have
the time [willingness] to implement these
changes in the near future.
‣ The 3 instructors who reported that they had not
have taken any statistic courses in their
undergraduate and graduate training, appeared
more eager to learn what the 'right' way is.
Additional Time to Prepare for
Class
‣ 3 out of 11 instructors would like to use applets
or other additional technologies to teach statistics
‣ 3 out of 11 very interested in very real and
relevant data sets.
-
Some feel that the data in the textbook are that
relevant or real.
Some are not satisfy with the data found on the
web since it requires too much time cleaning up or
is not relevant
Mixed feeling about creating in class survey to use
as data
‣ 7 out of 11 instructors would like to create more
relevant group activities and projects
Some Suggestions By Community
Colleges for Their Colleagues
‣ Administer quizzes to test basic or important
skills
- First, have group discussion based on
homework that was due
- Then, give a quiz based on homework and
discussion
‣ Form a cohort or community of instructors at
community college with weekly or bi-weekly
meetings.
‣ Have a monthly or quarterly meeting among the
different community colleges.
‣ Begin to implement one part of GAISE every
semester (if not already doing so)
Further Steps To be Taken
‣ Interview at least 15 additional instructors
‣ Interview department dean or chair to get their
‣
perspectives on teaching statistics
Conduct student surveys regarding their general
feelings about statistics and the textbook
‣ Analyze additional exams and corresponding
textbook chapters to get a more comprehensive
picture of teaching statistics at community
colleges
‣ Create sample group activities, projects, exams
and lessons using very real data set and GAISE
‣ Create a partnership between UCLA professors
who are interested in how statistics is taught at
the community college and community college
instructors.